We went on a cruise in December 2008. I debated whether to take cloth or not and am really glad in the end that we didn't. The washing facilities were always heaving - huge cruise ship, not many washers. And I wouldn't have put anything more expensive than a terry square in them, TBH, judging by the state of some of the clothes that came out.
Washers on cruise ships are not quite like my lovely all singin', all dancin' Hotpoint.
And you'd obviously not be able to dry them outside on a cruise ship, even if you have an outside room - you don't want them blowing off into the ocean.